[Eeyore]

I think one of the biggest problems for engineering students is that the
maths is too often taught in abstraction, which makes it difficult to
understand what the point is much of the time. In my experience, it's often
been the case that the maths only started to make sense when I tried to
solve a real engineering problem with it.

I agree entirely.

Incidentally, the advent of programs like Mathcad actually renewed my interest
in mathematical modelling.

Graham

 

[Michael A. Terrell]

NOT whizzing, WIZ.

My web coffee supplier, coffeewhiz.com, has recently changed to
coffeewiz.com ;-)

I didn't say "whizzing", now did I? ;-)



--
Service to my country? Been there, Done that, and I've got my DD214 to
prove it.
Member of DAV #85.

Michael A. Terrell
Central Florida

 

[Joel Kolstad]

Ah, yes. J_0, Y_0, I_0, K_0. I remember those. Also erfc(eta) and
the infinite series of sines and cosines. Solutions to PDEs.

Bessel functions (and Legendre polynomials) are also used as basis functions
in some curve fitting applications -- some of the fancier RF modeling programs
will let you create a continuous function from, e.g., S-parametmer data using
regular old rational polynomial or something fancier like Legendre or Bessel.

The communication guys occasionally throw in erfc() when they're dealing with
bit error rates, although I think in every case I've seen it actually makes
the equation somewhat messier because of the additional scaling constants that
need to be thrown in.

The guys who wrote the first cut of programs such as HFSS, CST, EMpower, etc.
(all field solvers of various types) all required some high-powered
mathematics. Even SPICE gets pretty fancy when you're trying to obtain really
good convergence...

 

[Joel Kolstad]

And in an instant, he went straight from 20-seconds of theory 20
minutes of cookbook rules on frequency-domain/time-domain mappings:
"Differentation in frequency domain is equivalent to ...."

Not to be a wet blanket, but as least in my college curriculum the *signal
processing* class assumed you had already gone through the long-winded
lectures and exercises on Fourier (back in a "signals and systems" class) and
also just had a "quick review."

"When...oh when!!! ARE WE GOING TO ACTUALLY LEARN THIS STUF!! Anyone
can read a table, but is there no one ELSE here who feels like I do,
that they know a little but doesn't really KNOWWWW!!!!!..."

I had an analog electronics class where the professor, on multiple occasions,
would answer questions by saying, "You should have learned that back in EE
102!" (or some comparably low-numbered course) -- I imagine that's how he'd
have handled your query. Not very diplomatic, but often true.

The teaching assistant came to the rescue by explaining that it was
pointless to try to *really* teach us, that one needs to study theory
of distributions first, and even then, it's still a matter of active
research. Our heads would pop (at least mine would have).

OK, now I'm starting to think you just went to a bad school.

That being said, I had another professor who once said, "you have to know
everything before you can know anything," and there is some truth to that --
things like Laplace transforms have enough nuances that, even if your goal is
to be an expert with them, it's arguably better to learn a little about them,
*use* them for awhile, and *then* go back for a more in-depth study rather
than trying to have an exhaustively in-depth lecture about them first.

I never studied theory of distributions, so I still don't know what
Fourier transforms really are. But I do understand convulution and
filtering, and I am sure others will agree that, when you can explain
in simple terms at a birthday party why the TV needs to be tuned to
channel 3 or 4 to process the signal from the video recorder, it's a
good feeling.

Even as a kid I remember thinking to myself, "hmm... shouldn't there be a more
direct route to producing a picture than making the VCR act like a TV
transmitter? I bet it would create a better picture that way..."

I think forcing yourself to like the math is not a bad idea. The ratio
of career time to college time is a large number, especially if you
discount the non-technical courses that you were forced to take, and
you should keep this in mind. Study math in bite-size pieces, and tuck
each piece away as you conquer it. Learning on your own at a slower
pace is not the same as being force-fed in college.

Good advice.

---Joel

 

[Joel Kolstad]

Spice won't do the right analysis if you don't know what you are doing.

Wasn't there just a big debate between John and Jim about how John doesn't
need a simulator?

 

[John Popelish]

TuT wrote:




I agree entirely.

Incidentally, the advent of programs like Mathcad actually renewed my interest
in mathematical modelling.

Likewise. It provides a completely flexible methodology for
both defining the form of the model and the figure of merit
to be optimized. I have spent hundreds of hours, usually
successfully, modeling various physical situations.

My last was fitting a hyperbola function to a saturating
inductance, with one asymptote following the high
permeability part of the curve, and the second asymptote
following the saturated, low permeability part of the curve
and the knee between matched to the transition zone between
these two asymptotes. Not only did Mathcad help with
finding the coefficients of the general quadratic that
includes all conic sections, it solved the derivatives of
flux (up to the 5th, I think) and all the symbolic algebra
needed to transform the general formula into a form that is
specified by simple values. These were the inductance at
zero current, the inductance and current at the inductance
inflection point of the curve, and the infinite current
inductance. I now have a simple spice model for swinging
chokes.

 

[Jim Thompson]

Wasn't there just a big debate between John and Jim about how John doesn't
need a simulator?

IIRC the big difference is that John can breadboard, I can't.

...Jim Thompson

 

[[email protected]]

IIRC the big difference is that John can breadboard, I can't.

...Jim Thompson

Oh breadboarding isn't so hard! You can pick up the skill in no time.

Hardest part for me is re-inserting a resistor that has its leads bent
from being inserted and removed from the breadboard too much.

 

[Jim Thompson]

Oh breadboarding isn't so hard! You can pick up the skill in no time.

Hardest part for me is re-inserting a resistor that has its leads bent
from being inserted and removed from the breadboard too much.

I used to breadboard chip designs. See...

http://analog-innovations.com/SED/BreadBoard.jpg

for about ONE-THIRD of the PCB set-up I used back then.

Now-a-days the device count and operating speeds preclude such
convenience, so I must simulate only.

...Jim Thompson

 

[JeffM]

I used to breadboard chip designs. See...
http://analog-innovations.com/SED/BreadBoard.jpg

Hollywood would HATE that board.
"Cut the BLUE wire."

 

[Eeyore]

Oh breadboarding isn't so hard! You can pick up the skill in no time.

It *would* be difficult for a cretin like Jim though. Especially if his
Alzheimers gets any worse.

Graham

 

[[email protected]]

Academic "engineers" love complex math, calculus and stuff. As a
working circuit designer, I don't use calculus at all (except in
understanding the basic concepts, integration and differentiation and
differential equations aka closed loops) and could mostly get by with
a 4-function calculator with square root. A little basic algebra is
handy. For anything really complex and nonlinear - and everything is
nonlinear - simulation is the way to go. A good feel for signal
processing - Fouriers, convolution, mixing and modulation, stuff like
that, is invaluable, but "feel" is usually enough.

Design is an emotional, qualitative activity, and analysis is an
intellectual, quantitative activity, and Spice can do most of your
analysis for you. So get that degree somehow and get out in the real
world and design real stuff. Send me a resume.

John

I should clarify that I have been working in the real world for about
3.5 years. You're right, I've never used any of this high-level stuff
on the job. I'm just frustrated at my Master's class!

 

[Jim Thompson]

Hollywood would HATE that board.
"Cut the BLUE wire."

That's Teflon insulation... me, the klutz, can't burn it with an iron
;-)

...Jim Thompson

 

[John Larkin]

Oh breadboarding isn't so hard! You can pick up the skill in no time.

Hardest part for me is re-inserting a resistor that has its leads bent
from being inserted and removed from the breadboard too much.

Jim is designing ICs, and he can't breadboard in any meaningful way.

In fact, I rarely breadboard, and then only very small snippets, just
to see how a part behaves. I'd never breadboard a full product... it's
better to go straight to the final multilayer board, and let the
people in production build the first one for me. I don't simulate
much, either, and again that would be just a snippet of the entire
product.

Jim has to simulate because the cost of spinning a wafer design is too
high; he can't kluge, either!

John

 

[Jim Thompson]

Jim is designing ICs, and he can't breadboard in any meaningful way.

In fact, I rarely breadboard, and then only very small snippets, just
to see how a part behaves. I'd never breadboard a full product... it's
better to go straight to the final multilayer board, and let the
people in production build the first one for me. I don't simulate
much, either, and again that would be just a snippet of the entire
product.

Jim has to simulate because the cost of spinning a wafer design is too
high; he can't kluge, either!

John

I have "blue-wired" some chips... it's called ion milling... but it's
VERY expensive, yet a quick way to see if a patch is going to work.

...Jim Thompson

 

[Eeyore]

In fact, I rarely breadboard, and then only very small snippets, just
to see how a part behaves. I'd never breadboard a full product... it's
better to go straight to the final multilayer board, and let the
people in production build the first one for me.

Likewise.

The pcb is often critical to the correct operation of the product. Breadboarding
has relatively little applicability any more.

Graham

 

[Terry Given]

Likewise. It provides a completely flexible methodology for both
defining the form of the model and the figure of merit to be optimized.
I have spent hundreds of hours, usually successfully, modeling various
physical situations.

My last was fitting a hyperbola function to a saturating inductance,
with one asymptote following the high permeability part of the curve,
and the second asymptote following the saturated, low permeability part
of the curve and the knee between matched to the transition zone between
these two asymptotes. Not only did Mathcad help with finding the
coefficients of the general quadratic that includes all conic sections,
it solved the derivatives of flux (up to the 5th, I think) and all the
symbolic algebra needed to transform the general formula into a form
that is specified by simple values. These were the inductance at zero
current, the inductance and current at the inductance inflection point
of the curve, and the infinite current inductance. I now have a simple
spice model for swinging chokes.

nice. fancy sharing?

Cheers
Terry

 

[[email protected]]

Thus the MIT method... math necessary for the engineering topic at

hand is taught (in a math class) at the same time.

So I'm still a wiz at Calculus though I rarely use it.

...Jim Thompson

Nice to hear it from a real engineer. The method has nothing to do with
MIT though. It is an old Prussian
style education method, where a number of subjects are taught at the
same time in sync (say surface integrals are introduced just before
Maxwell eq's are discussed). Works great: you see the same topic in
(usually several) different classes one after another. Now back to
reality: very few schools other than MIT can afford this. I teach math
at an engineering college (don't laugh or get angry with me now). All
we hear is: keep students happy at all costs. That means: let them pick
what they take and when they do that. Hard to pull that MIT trick here.
I do spice my lectures with a bunch of examples from, say circuits, or
mechanical engineering (gear tooth profiles, for example, or quantum
chemistry stuff and telegraphy equation when I teach PDEs) but most of
the time students do not understand applications themselves (it is hard
to get them excited about transmission lines and microstrips when I
only get blank stares from seniors when I say `transmission
line'---they are all digital design majors nowadays). You can tell, I
love engineering (and I work with a lot of `academic engineers') and I
do try to get students excited about math but my usual approach (which
finally relates to the topic of this thread) is rather subdued:

1) Analysing stuff in your head IS math or at least very akin to it.
2) Engineers rarely SEE what they are dealing with so for the most part
they, too are dealing in abstractions.

As someone in this thread has put it, `You just need a basic feel for
Fourier transforms, and frequency domain stuff'. And where exactly
would you get that `feel' without studying math?

Alex

PS. Those who rely on SPICE simulations too much, just what do you guys
do when the sim does not converge? I am not trying to pull Bob Pease on
you or aything

 

[[email protected]]

Also... what's the deal with (in)homogeneous boundary conditions? I

Must admit one thing. Have forgotten. Sorry!

This is easy: if you have two solutions satisfying homogeneous BC's
their sum still satisfies the same BC's (also called the superposition
property). Not true for nonhomogeneous BC's.

Why is superposition needed? Well, how do you solve the equation? By
pieces (called elementary solutions) that are then ADDED together in a
Fourier series. If addition destroyed the solution one would not get
very far.

A rotten mathematician such as myself would have said that the
solutions of a HBC problem form a space and linearize the problem.

Alex

 

[Jim Thompson]

...Jim Thompson

Nice to hear it from a real engineer. The method has nothing to do with
MIT though. It is an old Prussian
style education method, where a number of subjects are taught at the
same time in sync (say surface integrals are introduced just before
Maxwell eq's are discussed). Works great: you see the same topic in
(usually several) different classes one after another. Now back to
reality: very few schools other than MIT can afford this. I teach math
at an engineering college (don't laugh or get angry with me now). All
we hear is: keep students happy at all costs. That means: let them pick
what they take and when they do that. Hard to pull that MIT trick here.
I do spice my lectures with a bunch of examples from, say circuits, or
mechanical engineering (gear tooth profiles, for example, or quantum
chemistry stuff and telegraphy equation when I teach PDEs) but most of
the time students do not understand applications themselves (it is hard
to get them excited about transmission lines and microstrips when I
only get blank stares from seniors when I say `transmission
line'---they are all digital design majors nowadays). You can tell, I
love engineering (and I work with a lot of `academic engineers') and I
do try to get students excited about math but my usual approach (which
finally relates to the topic of this thread) is rather subdued:

1) Analysing stuff in your head IS math or at least very akin to it.

Of course. I even _dream_ circuits ;-) I think I've been at this
stuff so long I can _simulate_ circuits directly in my head and
quickly find the faults.

2) Engineers rarely SEE what they are dealing with so for the most part
they, too are dealing in abstractions.

I must admit to have an inability for certain abstractions... atomic
physics gave me great heartburn ;-)

As someone in this thread has put it, `You just need a basic feel for
Fourier transforms, and frequency domain stuff'. And where exactly
would you get that `feel' without studying math?

And lots of practice. I was fortunate enough to grow up in the
"backward" state of West Virginia, where basics was ALL that was
taught; and a wonderful Algebra teacher named Truchovesky who _forced_
me to think, and kept me loaded up with book after book, where I
worked _every_ problem in them. Then likewise with Geometry and
Trigonometry.

Alex

PS. Those who rely on SPICE simulations too much, just what do you guys
do when the sim does not converge? I am not trying to pull Bob Pease on
you or aything

More and more, my consulting includes looking over the shoulder of
young bucks, trying to teach. Unfortunately most can't "think"
anywhere but in front of the tube... no hands-on experience whatsoever
:-(

...Jim Thompson